Problem: Solve for $r$. $16-2r=-3r+6r+1$ $r=$
Solution: We need to manipulate the equation to get $ r $ by itself. $\begin{aligned} 16-2r&=-3r+6r+1 \\\\ 16-2r&=3r+1&&\gray{\text{Combine like terms.}}\\\\ 16-2r {-3r} &= 3r+1{-3r} &&\gray{\text{Subtract 3r from each side.}}\\\\ -5r+16&=1 &&\gray{\text{Combine like terms.}}\\\\ -5r+16{-16} &= 1{-16} &&\gray{\text{Subtract 16 from each side.}}\\\\ -5r &=-15 &&\gray{\text{Combine like terms.}}\\\\ \dfrac{-5r}{{-5}} &= \dfrac{-15}{{-5}} &&\gray{\text{Divide each side by -5.}}\\\\ r &= {3} &&\gray{\text{Simplify.}} \end{aligned}$ The answer: $ r= { 3 }~~~~~~~~$ [Let's check our work!]